I would say that causality is backwards. Radar existed in the 1930s but was never seriously developed. But imagine a world where it had been and that battleships had radar-directed AA guns, perfectly do-able in the 1940s. It would very early on in WW2 have been "proven" that aircraft couldn't touch a battleship at sea and so noone would have bothered to invent carriers. Air superiority became a thing because battleships were helpless against it, not the other way round.
Carriers were invented well before this. And would have been invented regardless, as they were useful for more than just sinking battleships. The fact that they could sink battleships resulted in them becoming the preeminent surface combatant.
But carriers were useful for scouting, for land attack, for defense against enemy aircraft, for anti-submarine warfare, for killing smaller surface combatants (like destroyers).
Followed by using the barely understood jump drive, resulting in SDF-1, two nearby aircraft carriers and the entire island being transported behind the orbit of Pluto. :D
I also really liked the part where a couple of the main characters got stranded in an isolated part of the humongous ship right after the jump & had to fish for a frozen tuna floating in front of airlock to get some food while waiting to be rescued. :)
It was useless with the overly-complicated battle plans and bad luck of the IJN. (Yamamoto dictated such complex maneuvers that the captains lost track of the objective at both Midway and Leyte Gulf.)
Had the Yamato and Musashi not been distracted and just turned into Leyte Gulf as planned, the American landing craft were sitting ducks. Instead, the Yamato went home, and the Musashi was swarmed and sunk.
That's overstating it a bit.
Six battleships, seven cruisers, and 21 destroyers were prepared to meet the Japanese force, and they'd have been under air attack either way.
An underdog nation, with pride in "punching above its weight class", placed a lot of hope and pride in a single piece of military hardware.
It was the largest battleship ever built, key to the Japanese strategy in WWII. American battleships' guns and armor were limited by the need for American battleships to fit through the Panama Canal. Knowing this, Japan built the much larger Yamato class with armor impervious to the 16" guns on American battleships. Her 18" guns could cut through any American battleship with ease. The Yamato was really a marvel.
Of course, it was utterly useless in battle against the American navy. Its WWI-era fire control systems were decades behind those of American battleships, especially the Iowa class, and of course more importantly WWII showed the world that battleships were helpless against naval air superiority. The Yamato was sunk by American planes, having never fired a shot against an opposing battleship.
The Yamato has remained in Japanese imagination, though, most notably in the long-running anime Uchu Senkan Yamato / Space Battleship Yamato / "Star Blazers".